Problem: Express this quotient in scientific notation: ${\frac{1.680\times 10^{-2}} {4.0\times 10^{1}}}$
Answer: Start by collecting like terms together. $= {\frac{1.680} {4.0}} \times{\frac{10^{-2}} {10^{1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.42 \times 10^{-2\,-\,1}$ $= 0.42 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.42$ is the same as $4.20 \div 10$ , or $4.20 \times 10^{-1}$ $ = {4.20 \times 10^{-1}} \times 10^{-3} $ $= 4.20\times 10^{-4}$